Question: Simplify the following expression: $\dfrac{70n^2}{120n^4}$ You can assume $n \neq 0$.
Explanation: $ \dfrac{70n^2}{120n^4} = \dfrac{70}{120} \cdot \dfrac{n^2}{n^4} $ To simplify $\frac{70}{120}$ , find the greatest common factor (GCD) of $70$ and $120$ $70 = 2 \cdot 5 \cdot 7$ $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(70, 120) = 2 \cdot 5 = 10 $ $ \dfrac{70}{120} \cdot \dfrac{n^2}{n^4} = \dfrac{10 \cdot 7}{10 \cdot 12} \cdot \dfrac{n^2}{n^4} $ $\phantom{ \dfrac{70}{120} \cdot \dfrac{2}{4}} = \dfrac{7}{12} \cdot \dfrac{n^2}{n^4} $ $ \dfrac{n^2}{n^4} = \dfrac{n \cdot n}{n \cdot n \cdot n \cdot n} = \dfrac{1}{n^2} $ $ \dfrac{7}{12} \cdot \dfrac{1}{n^2} = \dfrac{7}{12n^2} $